gwkokab.models.redshift

Classes

MadauDickinsonRedshiftModel	Redshift distribution for compact binary mergers modeled after the Madau-
PowerlawRedshiftModel	Redshift distribution for compact binary mergers modeled as a power law modulated

Package Contents

class gwkokab.models.redshift.MadauDickinsonRedshiftModel(z_max: jax.Array, kappa: jax.Array, gamma: jax.Array, z_peak: jax.Array, *, validate_args: bool | None = None)

Bases: _RedshiftModel

Redshift distribution for compact binary mergers modeled after the Madau- Dickinson star formation rate, modulated by the cosmological volume element.

The probability density function is defined as:

\[\begin{split}p(z) \propto \frac{dV_c/dz(z) \cdot (1 + z)^{\kappa - 1}}{1 + \left(\\frac{1 + z}{1 + z_{peak}}\right)^{\gamma}}, \ \qquad 0 \leq z \leq z_{max}\end{split}\]

where:

• dV_c/dz is the differential comoving volume element,

• gamma is the high-redshift slope,

• kappa is the low-redshift slope,

• z_max is the upper redshift cutoff.

• z_peak is the redshift at which the merger rate peaks,

This distribution is normalized numerically on a fixed redshift grid.

log_psi_of_z(z: jax.Array) → jax.Array

Evaluate the psi function at a given redshift.

\[\ln\psi(z) = \kappa \ln(1 + z) + \ln\left(1 + (1 + z_{peak})^{\gamma}\right) - \ln\left((1 + z_{peak})^{\gamma} + (1 + z)^{\gamma}\right)\]

Parameters:

z (ArrayLike) – Redshift(s) to evaluate.

Returns:

Values of the psi function.

Return type:

ArrayLike

class gwkokab.models.redshift.PowerlawRedshiftModel(z_max: jax.Array, kappa: jax.Array, *, validate_args: bool | None = None)

Bases: _RedshiftModel

Redshift distribution for compact binary mergers modeled as a power law modulated by the cosmological volume element.

The probability density function is defined as:

\[p(z) \propto \frac{dV_c/dz(z) \cdot (1 + z)^{\kappa - 1}}}, \qquad 0 \leq z \leq z_{max}\]

where:

• dV_c/dz is the differential comoving volume element,

• is the redshift evolution power-law index,

• z_max is the upper redshift cutoff.

This distribution is normalized numerically on a fixed redshift grid.

Parameters:

• kappa (float) – The power-law exponent \(\kappa\).

• z_max (float) – The maximum redshift (upper limit of the support).

log_psi_of_z(z: jax.Array) → jax.Array

Evaluate the psi function at a given redshift.

\[\ln\psi(z) = \kappa \ln(1 + z)\]

Parameters:

z (ArrayLike) – Redshift(s) to evaluate.

Returns:

Values of the psi function.

Return type:

ArrayLike